Actually, I remember reading that the WWII B-17 used electrically operated flight-control surfaces instead of hydraulics, in part because it's harder to shoot a hole in a wire than in a hydraulic hose. Those were some tough planes!

A steering wheel is "Roughly Speaking" a "2D" device - you move it "To the Left" or "To the Right" and the car "Follows" it. But more importantly, when you do NOT move it to the Right or Left, the car stays on the course that it is already on, (Whether that be on a curve or straiht ahead).
A Joy Stick, (If you disregard its "North/South" movement, which, you could well argue could be used for accelerating, ("Up"), or for Braking, ("Down"), does not have a "Rest" position and you would be forced to "Hold it in position" all the time.
Now if you could "Spring Load" it back to its neutral position, I might buy that.
Tony

You bring up some great points. Just look at how the keyless start system on newer cars causes confusion to most drivers. By most I mean the average driver that only thinks of a car as an appliance that takes you from A to B. On many cars you need to hold the "Start" button down a few seconds to shut the engine off. With the standard key you just need to turn it counterclockwise which can take less than a second. One method is cool and "new", while the other is old but much more natural.
When I wrote earlier about my BMW launching itself when coolant shorted the throttle position sensor pins on the ECU, no one would ever imagine that that would happen. And evidently BMW didn't expect anything to ever go wrong with the throttle position input so there was no safety check against pressing the brake and accelerator at the same time. Thankfully I instinctively threw the shiter into neutral but how many people would have done the same thing when a 282HP V8 all of a sudden decides to go wide-open-throttle by itself? Now this was a "mechanical failure" (the coolant temperature sensor failed resulting in the coolant to enter the wiring harness) that resulted in a software failure. We can add as many MCU or MPUs on a car as we want but we really need to factor in failsafe systems. Losing steering control on a car is much worse than the lighter fuse blowing out.
As for reliability, my father has a 1971 Corvette (All-original) that starts right up even in -25degreesC weather every single time. On the other hand, my BMW had an air pump whose only purpose was to blow cold air onto the O2 sensors on startup to avoid a check-engine-light from appearing. That's right...on startup only. Of course the pump died and it cost $500+ for a replacement...all this just to trick the O2 sensors for a brief period of time!
Technology is great, that's why many of us became engineers but sometimes there are solutions proposed without a problem.

First thing I did in the test drive last year when I found I couldn't get a new pickup truck without power brakes and power steering was run it up to 15 MPH, turn off the key, and demonstrate that I could steer it and stop it. After a few years designing burner safety controls, where the overriding design consideration is ironclad proof that every physically possible component failure leads to a safe condition, I'm far more concerned with failure mode effects than failure probabilities. As for stuff like power windows, it's just more crap to break. What ever happened to KISS?

A few thoughts to Bill's original question:
One big problem with anything new in the car is the variation between manufacturers. Look at the trouble Audi had in the 1980's, primarily chalked up to the pedal cluster placement being shifted a bit relative to big American cars... and that's even with basically the same control system. It's daunting to imagine the problems people will have with several variations on the theme among different models, esp. in rental cars. Anything unexpected/unintuitive in emergency situations will make outcomes worse.
Any changes here will have to go though some sort of standardization process. That alone could be a big enough barrier to stall progress.
Reliability, for me, is the main barrier though. I've had a few older cars and when problems arose with mechanical things the situation was minor and with a lot of warning (e.g. seepage around the steering rack gasket). Most of the problems related to electronics - and not the devices as much as the connectors failing. By and large the mechanical systems hold up pretty well for 20 years even in extreme heat (south Florida).

The question or point isn't that a steering wheel could be replaced by something; of course it could. But the question should be WHY do you want to replace it? Other than design and manufacturability improvements by having wires instead of a linkage, is there some actual shortcoming or problem with the steering wheel that someone is trying to address??
Don't brand the folks here as Luddites (or -ish) for being skeptical. There has to be, first off, a good reason to change something, and second, the replacement has to meet or exceed all of the performance of the original and solve some additional problems.
The thread is quite long, so I'm sorry if I missed someone pointing out the problems, but it's a waste of time to talk about insufficient and unneeded solutions to problems that don't exist.